This handout photo provided by Collin County, Texas shows Texas Attorney General Kenneth Paxton, who was booked into the county jail Monday, Aug. 3, 2015, in McKinney, Texas. A grand jury last week indicted

AUSTIN - Gov. Greg Abbott brushed off the idea Monday that indicted Attorney General Ken Paxton should resign, while the state GOP chairman said Texas' chief law enforcement officer "absolutely" should stay in office while he faces the charges against him.

Their comments came on the heels of a poll indicating that 62 percent of likely Republican voters in Texas think Paxton should resign after being indicted on alleged securities law violations.

"I haven't seen the poll," said Abbott when asked about the poll during a visit to an elementary school to mark the first day of school.

"The way I feel about anything like that, having been a judge myself, I think the process needs to work its course. I think everyone is innocent until proven guilty," Abbott added.

But Abbott, who was elected governor after serving on the Texas Supreme Court and then as attorney general, did not tie himself too tightly to Paxton.

Asked whether he had spoken to Paxton since his indictment weeks ago, Abbott said, "I don't think I have."

Paxton has said he expects to be fully vindicated in the case and his lawyer, Joe Kendall, in a statement voiced appreciation for Abbott's comments.

"I agree with Governor Abbott and appreciate his perspective. This is America, in which a person is presumed innocent. I too am confident in the process. In the meantime, Attorney General Paxton will continue to work hard for the citizens of Texas," Kendall said.

Republican Party of Texas Chairman Tom Mechler looked askance at the record of the firm that did the poll and said in an interview that Paxton is "a very distinguished leader of our state" who's entitled to the presumption that he's innocent until proven guilty.

"I absolutely do not think he should step down," Mechler said, adding that he frequently speaks to Republicans. "I can tell you for sure there is no groundswell of Republicans … regarding anything about a resignation. In all those speaking engagements, nobody has even asked me that question."

Mechler said that "most Republicans are very skeptical of what we perceive to be a very sloppy process of what we've witnessed so far."

Texas Democrats continued their call for Paxton to step down, citing the poll by Florida-based Gravis Marketing, which also found that 53% of self-identified tea party voters think Paxton should resign.

However, Gabriel Torre of Seabrook, who helped organize the tea party in Clear Lake years ago although he doesn't speak for it, said Paxton is entitled to the presumption of innocence.

"You're always innocent until proven guilty. … We've got a good system in America," Torre said. "Should he resign? If he's proven guilty, then he should apologize to everybody and resign."

Former state Republican chairman George Strake of Houston said he likes and voted for Paxton. He said he does not know the details of the accusations but doesn't think Paxton should resign unless proven guilty.

"I'm not ready to have him walk out of office right away. I want it proved that he actually did something wrong," Strake said.